Zahn et al. 1974
Zahn, J.-P., J. Toomre, E.A. Spiegel, and D.O. Gough, 1974: Nonlinear cellular motions in Poiseuille channel flow. J. Fluid Mech., 64, 319-346, doi:10.1017/S0022112074002424.
We expand the equations describing plane Poiseuille flow in Fourier series in the co-ordinates in the plane parallel to the bounding walls. There results an infinite system of equations for the amplitudes, which are functions of time and of the cross-stream co-ordinate. This system is drastically truncated and the resulting set of equations is solved accurately by a finite difference method. Three truncations are considered: (I) a single mode with dependence only on the downstream co-ordinate and time, (II) the mode of (I) plus its first harmonic, (III) a single three-dimensional mode. For all three cases, for a variety of initial conditions, the solutions evolve to a steady state as seen in a particular moving frame of reference. No runaways are encountered.
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Zahn, J.-P., Toomre, J., Spiegel, E.A., and Gough, D.O.: Nonlinear cellular motions in Poiseuille channel flow, J. Fluid Mech., 64, 319-346, doi:10.1017/S0022112074002424, 1974.
Zahn, J.-P., J. Toomre, E.A. Spiegel, and D.O. Gough (1974), Nonlinear cellular motions in Poiseuille channel flow, J. Fluid Mech., 64, 319-346, doi:10.1017/S0022112074002424.
Zahn, J.-P., J. Toomre, E.A. Spiegel, and D.O. Gough, 1974: Nonlinear cellular motions in Poiseuille channel flow. J. Fluid Mech., 64, 319-346, doi:10.1017/S0022112074002424.
Zahn, J.-P., Toomre, J., Spiegel, E.A., & Gough, D.O. 1974, J. Fluid Mech., 64, 319, doi:10.1017/S0022112074002424.
Zahn J-P, Toomre J, Spiegel EA, Gough DO. Nonlinear cellular motions in Poiseuille channel flow, J Fluid Mech 1974;64:319-346. doi:10.1017/S0022112074002424.
J.-P. Zahn, J. Toomre, E.A. Spiegel, D.O. Gough, J. Fluid Mech. 64, 319-346, doi:10.1017/S0022112074002424 (1974).
